Transport in a Luttinger liquid with dissipation : two impurities.

We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter $K$, and the deviation from the resonance condition is obtained. For weak dissipation and $1/2lKl1$, the conduction shows a nonmonotonic increase as a function of temperature or voltage. For strong dissipation the conduction increases monotonically but is exponentially small.